Robust method of metrology for direct phase measurement for nano-antennas

. Optical metasurfaces allow the development of original and more and more complex optical functions. They are therefore facing a design and characterization problem. Indeed, they are more and more composed of complex patterns, with different types of antennas and non-periodic. This is why it is important to build libraries of nano-structures that can be used as building blocks to compose optical functions. Therefore, we propose a direct phase measurement metrology method for optical nanostructures. Using lateral shift interferometry, our technique allows to simultaneously characterize in amplitude and phase nano-antennas of all types, shapes and materials, and thus to experimentally establish a library of nano-antennas. Our method brings an additional tool in the design of nano-antennas, which completes the existing simulation tools, by allowing to test all types of nano-antennas.


Metasurfaces
Developed over the last twenty years, optical metasurfaces represent an important innovation, a new tool allowing a new approach to the development of optical functions.Compact, they can replace bulk optics by mimicking conventional optical functions such as lenses, half-wave plates or doublets [1][2][3] ; sometimes even improving these functions (by correcting chromatism for example [4]) or making them more complex (for example, lenses with wavelength-dependent focal lengths [5]).Moreover, they allow innovation by creating new functions (holography [6], wavelengthdependent phase mask [7],...) This is made possible by the nanostructuring of metasurfaces composed of meta-atoms, sub-wavelength antennas, which by their geometries and/or directions make it possible to act on the incident wavefront and generate an aberrant but controllable reflection or refraction.Different forms of nano-antennas (dielectric, metal, metal-insulator-metal) have been used to achieve this control, which allows to control the amplitude, phase and/or polarisation of the output light.

Characterization of metasurfaces
For the moment, the study of metasurfaces has focused both on their conception and design, whether via direct (RWCA, FDTD with software such as Reticolo [8], BMM [9], PyRCWA) or inverse (Inverse Design [10]) simulations, and on the functional characterisation of the systems produced.However, direct measurement of the phase induced by a nano-antenna before integration into a function is not achieved.Therefore, we propose a robust phase metrology method using lateral shift interferometry, based on the PISTIL interferometer (PISton and TILt).[11]

The interferometer PISTIL
The strength of this interferometer is to be able to measure simultaneously and redundantly the phase shift induced by n samples of different nano-antennas placed side by side on a hexagonal mesh.As described in the Figure 1, the light entered the interferometer.Thanks to a mask allowing to lacunarize the beam into n smaller beams and to a hexagonal diffraction grating, which sends the +1 and -1 orders in three different directions, spaced of 60°, for a nano-antenna sample, we can obtain on the same image, the interference figures of with its six neighbours.A Fourier treatment is then necessary to reconstruct the phase.

Test of the interferometric technique
We propose to test this metrological technique in the MWIR with MIM antennas (Metal-Insulating-Metal, here Au-ZnS-Au).The tests were carried out on thirty-seven nano-antennas, used in reflection, for which we varied the reflectivity and phase according to the wavelength, by varying the period, length and width of the gold nanoantennas.
By scanning at wavelength between 3 and 4 µm our sample, and using the PISTIL interferometer, we can reconstruct the phase induced by the geometry studied as well as that of its neighbours in a single measurement.
When talking about metrology, it is imperative to talk about reference.In our case of using the PISTIL interferometer, with a wavelength scan, we have chosen to use a gold mirror as a reference.The latter has the advantage of being sufficiently constant in phase and reflectivity over the wavelength range considered.It also allows an absolute measurement of the piston.In this first experiment, Tip/Tilt measurements are not directly used because our sample creates only pistons, but they could be exploited in future work The characterisation of our test sample is done in two steps.First, the reflectivity characterisation of the nanostructures is carried out using FTIR (Fourier Transform Infra-Red).Then, the PISTIL interferometer is used to trace back to the phase.For this, several interferograms are acquired at regular intervals between 3 and 4 µm.In Fourier space, it is then possible to extract first order harmonics in the three directions 0°, 60° and 120°.For each direction, and thus for each extracted harmonic, we can return to the real space and thus find the phase shift induced in this direction by the various samples.By assembling the phase shift obtained in each direction, a phase shift map Δ is obtained.Finally, the phase is calculated by the following matrix calculation: with  the estimated sample phase,  + the pseudo-inverse of the propagation matrix in the interferometer and Δ the reconstructed phase shift

Conclusion
Direct measurement of the nano-antenna phase can be achieved using the PSITIL interferometer.It allows the direct and simultaneous characterisation of several types of nanostructure, before their integration into an optical function, regardless of the material or type of the antennas This robust interferometric phase measurement technique thus allows the development of a library of nano-structures characterised experimentally in phase and amplitude.It completes the existing simulation tools, allowing to test all types of nano-antennas.Fig. 1.Illustration of the interferometer PISTIL : the light locally out of phase with the nano-antennas enters the interferometer.It first encounters a hole mask, making it possible to lacunarize the beam and to go from a single beam locally out of phase to 7 beams each having its own phase.These 7 beams then cross a diffracting grating, allowing to send the -1 and +1 orders in three different directions spaced 60° each.For a nano-antenna sample, we then obtain on the same image, the interference figures of with its six neighbours.By treatment of Fourier, we can then reconstruct the phase.In this figure, to help understanding the operation, we have colored the different beams from the different structures to analyse.